Horiuchi Toshio 堀内利郎

… Alternative Names

Researcher Number	80157057
Other IDs
External Links
Affiliation (Current)	2020: 茨城大学, 理工学研究科(理学野), 教授
Affiliation (based on the past Project Information) *help	2018 – 2020: 茨城大学, 理工学研究科(理学野), 教授 1995 – 2017: 茨城大学, 理学部, 教授 2005: 茨成大学, 理学部, 教授 1996: 茨城大学理学部, 教授 1994: 茨城大学, 理学部, 助教授 1991: 茨城大学, 理学部, 助教授 1987: 茨城大学, 理学部, 助手
Review Section/Research Field	Principal Investigator Basic analysis / 解析学 / Basic analysis / Basic Section 12020:Mathematical analysis-related Except Principal Investigator Basic analysis / 解析学 / Basic analysis
Keywords	Principal Investigator 退化楕円型方程式 / 非線形楕円型方程式 / ソボレフの不等式 / 重み付きソボレフ不等式 / CKN型不等式 / ソボレフ不等式 / ハーディ不等式 / ミッシングターム / 重み付きソボレフの不等式 / degenerate elliptic equation … More Except Principal Investigator caloric morphism / 熱方程式の解を保つ変換 / Appell変換 / 熱方程式 / 調和解析 / 関数空間 / Appell transformation / heat equation / ウェーブレット / 実解析 / 波動方程式の解を保つ変換 / Bateman変換 / 変動指数 / Hardy空間 / 作用素 / 代作用代数 / エントロピ- / Toeplitz作用素 / Schrodinger / ポテンシャル / 相対容量 / シュタルク効果 / 波動作用素 / 漸近的完全性 / 散乱全断面積 / 準古典近似 / 影散乱 / フォン・ノイマン環 / 因子環 / 非可換力学系 / 非可換確率論 / 非可換エントロピー / ランダム・ウォーク / 自由確率論 / 多重線形 / 多重線形作用素 / ベイトマン変換 / 調和解析学 / 実解析学 / 分数べき積分 / 特異積分 / Orlicz空間 / Campanato空間 / Morrey空間 / Hardy-Orlicz族 / BMO / 特異積分作用素 / 埋め込み定理 / 多重熱作用素の解 / ソボレフ空間 / 重み付き空間 / Triebel-Lizorkin空間 / 非線型波動方程式 / 非線型変分問題 / Sobolev-Lieb-Thirring不等式 / 非線型方程式 / シュレディンガー方程式 / Sobolev space / wavelet / weighted space / Triebel-Lizorkin space / 積分作用素 Less

A new refinement allowing infinite-order degeneration and explosion of weighted classical inequalities and its application to variational problemsPrincipal InvestigatorOngoing
- Principal Investigator
  
  堀内利郎
- Project Period (FY)
  2020 – 2024
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 12020:Mathematical analysis-related
- Research Institution
  Ibaraki University
古典的不等式の精密化に基づく非線型楕円型方程式の定性的研究Principal InvestigatorOngoing
- Principal Investigator
  
  堀内利郎
- Project Period (FY)
  2016 – 2019
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Ibaraki University
実解析・調和解析に由来する関数空間の理論の深化と応用Ongoing
- Principal Investigator
  
  中井英一
- Project Period (FY)
  2015 – 2019
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Basic analysis
- Research Institution
  Ibaraki University
Research on transformations preserving solutions of the heat equation, wave equation
- Principal Investigator
  
  Shimomura Katsunori
- Project Period (FY)
  2013 – 2015
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Ibaraki University
Refinement of classical inequalities and its application to elliptic variational problemsPrincipal Investigator
- Principal Investigator
  
  Horiuchi Toshio
- Project Period (FY)
  2012 – 2015
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Ibaraki University
Harmonic analysis based on function spaces with variable exponent and its applications
- Principal Investigator
  
  NAKAI Eiichi
- Project Period (FY)
  2012 – 2014
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Ibaraki University
The research of transformations which preserve the solutions of the heat equation and the wave equation.
- Principal Investigator
  
  SHIMOMURA Katsunori
- Project Period (FY)
  2010 – 2012
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Ibaraki University
Reseach on multilinear harmonic analysis and its applications
- Principal Investigator
  
  TACHIZAWA Kazuya
- Project Period (FY)
  2008 – 2011
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Hokkaido University
On the improvement of classical inequalities and its applications to nonlinear degenerate elliptic equationsPrincipal Investigator
- Principal Investigator
  
  HORIUCHI Toshio
- Project Period (FY)
  2008 – 2011
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Ibaraki University
The research of caloric morphism
- Principal Investigator
  
  SHIMOMURA Katsunori
- Project Period (FY)
  2007 – 2008
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Ibaraki University
The Study of caloric morphism
- Principal Investigator
  
  SHIMOMURA Katsunori
- Project Period (FY)
  2005 – 2006
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Ibaraki University
On the linearization of quasilinear degenerate elliptic equations and the structure of singular solutionsPrincipal Investigator
- Principal Investigator
  
  HORIUCHI Toshio
- Project Period (FY)
  2005 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Ibaraki University
A characterization of weighted Sobolev spaces and its applications
- Principal Investigator
  
  TACHIZAWA Kazuya
- Project Period (FY)
  2004 – 2006
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Hokkaido University
The research of caloric morphism
- Principal Investigator
  
  SHIMOMURA Katsunori
- Project Period (FY)
  2003 – 2004
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  IBARAKI UNIVERSITY
On the structure of singular solutions for degenerate elliptic equationsPrincipal Investigator
- Principal Investigator
  
  HORIUCHI Toshio
- Project Period (FY)
  2002 – 2004
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  IBARAKI UNIVERSITY
The research of caloric morphism
- Principal Investigator
  
  SHIMOMURA Katsunori
- Project Period (FY)
  2001 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  IBARAKI UNIVERSITY
The research on degenerate elliptic partial differential equations by the method of real analysisPrincipal Investigator
- Principal Investigator
  
  HORIUCHI Toshio
- Project Period (FY)
  1999 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  IBARAKI UNIVERSITY
On the regularity of solutions for degenerate elliptic equationsPrincipal Investigator
- Principal Investigator
  
  HORIUCHI Toshio
- Project Period (FY)
  1997 – 1998
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  IBARAKI UNIVERSITY
作用素環上の非可換確率論の研究
- Principal Investigator
  
  日合文雄
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Ibaraki University
退化楕円型方程式の解の構造の研究Principal Investigator
- Principal Investigator
  
  堀内利郎
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Ibaraki University
退化楕円型方程式に関する諸問題の研究Principal Investigator
- Principal Investigator
  
  堀内利郎
- Project Period (FY)
  1995
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Ibaraki University
シュレ-ディンガー作用素のスペクトル理論の研究
- Principal Investigator
  
  田村英男
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Ibaraki University
作用素解析と作用素代数の研究
- Principal Investigator
  
  日合文雄
- Project Period (FY)
  1991
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Ibaraki University
複素構造に関連した解析学の研究
- Principal Investigator
  
  荷見守助
- Project Period (FY)
  1987
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Ibaraki University

[Book] 関数解析の基礎2005
- Author(s)
  堀内利郎
- Total Pages
  280
- Publisher
  内田老鶴圃
- Data Source
  KAKENHI-PROJECT-14540151
[Book] 関数解析の基礎2005
- Author(s)
  堀内利郎
- Total Pages
  296
- Publisher
  内田老鶴圃
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540146
[Journal Article] Kato’s inequalities for admissible functions to quasilinear elliptic operators A2019
- Author(s)
  Xiaojing Liu, Toshio Horiuchi
- Journal Title
  
  Mathematical journal of ibaraki University
  
  Volume: 51
- NAID
  130007687047
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K05189
[Journal Article] The equivalences among p-capacity, p-Laplace-capacities and Hausdorff measure.2018
- Author(s)
  Liu Xiaojing、Horiuchi Toshio
- Journal Title
  
  Mathematical Journal of Ibaraki University
  
  Volume: 50
- NAID
  130007465434
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-15H03621
[Journal Article] The equivalences among p-capacity, $p$-Laplace-capacities and Hausdorff measure.2018
- Author(s)
  Xiaojing Liu, Toshio Horiuchi
- Journal Title
  
  Mathematical Journal of Ibaraki University Volume
  
  Volume: 50
- NAID
  130007465434
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-16K05189
[Journal Article] The equivalences among <i>p</i>-capacity, <i>p</i>-Laplace-capacities and Hausdorff measure2018
- Author(s)
  Liu Xiaojing、Horiuchi Toshio
- Journal Title
  
  Math. J. Ibaraki Univ.
  
  Volume: 50 Issue: 0 Pages: 5-13
- DOI
  10.5036/mjiu.50.5
- NAID
  130007465434
- ISSN
  1343-3636, 1883-4353
- Language
  English
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K05189
[Journal Article] Remarks on Kato's inequality when $\Delta_p u$ is a measure2016
- Author(s)
  Xiaojing Liu, Toshio Horiuchi
- Journal Title
  
  Mathematical Journal of Ibaraki University
  
  Volume: 48 Pages: 45-61
- Peer Reviewed / Acknowledgement Compliant / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K05189
[Journal Article] Caffarelli-Kohn-Nirenberg 型不等式とその周辺2016
- Author(s)
  堀内利郎
- Journal Title
  
  数学
  
  Volume: 68
- NAID
  130006321022
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-15H03621
[Journal Article] radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p=12016
- Author(s)
  N. Chiba, T. Horiuchi
- Journal Title
  
  Proceedings of the Japan academy Series A Mathematical Sciences
  
  Volume: 92 Pages: 51-55
- NAID
  130005100042
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540157
[Journal Article] Remarks on Kato's inequality when $\Delta_p u$ is a measure2016
- Author(s)
  Xiaojing Liu and Toshio Horiuchi
- Journal Title
  
  Mathematical Journal of Ibaraki University
  
  Volume: 48
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-15H03621
[Journal Article] Remarks on the strong maximum principle involving p-Laplacian2016
- Author(s)
  Xiaojing Liu and Toshio Horiuchi
- Journal Title
  
  Hiroshima Mathematical Journal
  
  Volume: 46
- Peer Reviewed / Acknowledgement Compliant / Open Access
- Data Source
  KAKENHI-PROJECT-15H03621
[Journal Article] Caffarelli-Kohn-Nirenberg 型不等式とその周辺2016
- Author(s)
  堀内利郎
- Journal Title
  
  数学（日本数学会）
  
  Volume: 68 Pages: 1-23
- NAID
  130006321022
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540157
[Journal Article] Remarks on the strong maximum principle involvingp-Laplacian2016
- Author(s)
  Xiaojing Liu, Toshio Horiuchi
- Journal Title
  
  Hiroshima Mathematical Journal
  
  Volume: 46 Pages: 311-331
- Peer Reviewed / Acknowledgement Compliant / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K05189
[Journal Article] Radial symmetry and its breaking in the Caffarelli-Kohn- Nirenberg type inequalities2016
- Author(s)
  Naoki. Chiba, Toshio. Horiuchi
- Journal Title
  
  Proceedings of the Japan academy
  
  Volume: 92 (4) Pages: 51-55
- DOI
  10.3792/pjaa.92.51
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-16K05189
[Journal Article] On radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p=12015
- Author(s)
  N. Chiba, T. Horiuchi
- Journal Title
  
  Mathematical Journal of Ibaraki University
  
  Volume: 47 Pages: 49-63
- NAID
  130005100042
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540157
[Journal Article] Weighted Hardy inequalities with infinitely many sharp missing terms2014
- Author(s)
  Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai
- Journal Title
  
  Mathematical Journal of Ibaraki University
  
  Volume: 46
- NAID
  130004697044
- Peer Reviewed / Acknowledgement Compliant / Open Access
- Data Source
  KAKENHI-PROJECT-24540159
[Journal Article] Weighted Hardy inequalities with infinitely many sharp missing terms2014
- Author(s)
  Ando, Hiroshi; Horiuchi, Toshio; Nakai
- Journal Title
  
  Mathematical Journal of Ibaraki University
  
  Volume: 48 Pages: 9-29
- NAID
  130004697044
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540157
[Journal Article] Some properties of slowly increasing functions2014
- Author(s)
  Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai
- Journal Title
  
  Mathematical Journal of Ibaraki University
  
  Volume: 46
- NAID
  130004697043
- Peer Reviewed / Acknowledgement Compliant / Open Access
- Data Source
  KAKENHI-PROJECT-24540159
[Journal Article] Weighted Hardy inequalities with infinitely many sharp missing terms2014
- Author(s)
  Ando Hiroshi, Horiuchi Toshio, Nakai eiichi
- Journal Title
  
  Mathematical Journal of Ibaraki University
  
  Volume: 46 Pages: 9-30
- NAID
  130004697044
- Peer Reviewed / Acknowledgement Compliant / Open Access
- Data Source
  KAKENHI-PROJECT-24540157
[Journal Article] Some properties of slowly increasing functions2014
- Author(s)
  Ando Hiroshi, Horiuchi Toshio, Nakai eiichi
- Journal Title
  
  Mathematical Journal of Ibaraki University
  
  Volume: 46 Pages: 37-49
- NAID
  130004697043
- Peer Reviewed / Acknowledgement Compliant / Open Access
- Data Source
  KAKENHI-PROJECT-24540157
[Journal Article] Caffarelli-Kohn-Nirenberg inequalities involving critical and supercritical weights2012
- Author(s)
  T.Horiuchi, P. Kumlin
- Journal Title
  
  Kyoto Journal of Mathematics
  
  Volume: 52(4) Pages: 661-742
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540157
[Journal Article] The Caffarelli-Kohn-Nirenberg inequalities involving critical and supercritical weights2012
- Author(s)
  T.Horiuchi, P.Kumlin
- Journal Title
  
  Proceedings of the Japan Academy
  
  Volume: 88 Pages: 1-6
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540153
[Journal Article] The Caffarelli-Kohn-Nirenberg inequalities involving critical and supercritical weights2012
- Author(s)
  T. Horiuchi, P. Kumulin
- Journal Title
  
  Proceedings of the Japan Academy
  
  Volume: Vol.88, Ser. A No.1 Pages: 1-6
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540153
[Journal Article] CONSTRUCTION OF SLOWLY INCREASING FUNCTION2012
- Author(s)
  H. Ando, T. Horiuchi, E. Nakai
- Journal Title
  
  Scientiae Mathematicae Japonicae Online
  
  Volume: 25 Pages: 207-221
- NAID
  130007663411
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540157
[Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application2012
- Author(s)
  H. Ando, T. Horiuchi
- Journal Title
  
  Kyoto Journal of Mathematics
  
  Volume: 52(4) Pages: 759-796
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540157
[Journal Article] The Caffarelli-Kohn-Nirenberg type inequalities involving critical and supercritical weights, Proc.2012
- Author(s)
  Toshio Horiuchi and Peter Kumlin
- Journal Title
  
  Japan Acad. Ser.A Math. Sci
  
  Volume: 88(1) Pages: 1-6
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540149
[Journal Article] Peter Kumlin, On the Caffarelli-Kohn-Nirenberg-type inequalities involving critical and supercritical weights2012
- Author(s)
  堀内利郎
- Journal Title
  
  Kyoto Journal of Mathematics
  
  Volume: 52 Pages: 661-742
- URL
  http://projecteuclid.org/euclid.kjm/1352987531
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540169
[Journal Article] On the weighted rearrangement of functions and Degenerate Nonlinear elliptic equations2012
- Author(s)
  H. Ando, T. Horiuchi
- Journal Title
  
  Mathematical Journal of Ibaraki University
  
  Volume: 44 Pages: 17-31
- NAID
  130003373916
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540157
[Journal Article] Construction of slowly increasing functions2012
- Author(s)
  Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai
- Journal Title
  
  Scientiae Mathematicae Japonicae
  
  Volume: 75
- NAID
  130007663411
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540159
[Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application2012
- Author(s)
  安藤広, 堀内利郎
- Journal Title
  
  Kyoto Journal of Mathematics
  
  Volume: 52 Pages: 759-796
- URL
  http://projecteuclid.org/euclid.kjm/1352987533
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540169
[Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application2010
- Author(s)
  安藤広, 堀内利郎
- Journal Title
  
  Journal of Mathematics of Kyoto Unuv.(accepted) (未定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540153
[Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application2009
- Author(s)
  安藤広、堀内利郎
- Journal Title
  
  Journal of Mathematics of Kyoto University (巻頁未定)(印刷中)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540161
[Journal Article] Missingterms in the weighted Hardy-Sobolev inequalities and its application2009
- Author(s)
  安藤広、堀内利郎
- Journal Title
  
  Journal of Mathematics of Kyoto Unuv. (accepted) (未定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540153
[Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008
- Author(s)
  堀内利郎
- Journal Title
  
  Kyungpook Mathcmatical Journal 48-1
  
  Pages: 15-24
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540146
[Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008
- Author(s)
  Toshio Horiuchi
- Journal Title
  
  Kyungpook Mathematical Journal 48(1)
  
  Pages: 15-24
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540149
[Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008
- Author(s)
  堀内利郎
- Journal Title
  
  Kyungpook Mathematical Journal 48-1
  
  Pages: 15-24
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540161
[Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008
- Author(s)
  T. Horiuchi
- Journal Title
  
  Kungpook Mathematical J.
  
  Volume: 48-1 Pages: 15-24
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540153
[Journal Article] Kato's inequalities for degenerate quasilinear lliptic operators2008
- Author(s)
  Toshio Horiuchi
- Journal Title
  
  Kyungpook Mathematical Journal
  
  Volume: 48(1) Pages: 15-21
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540149
[Journal Article] Kato''s inequalities for degenerate quasilinear elliptic Operators2008
- Author(s)
  T. Horiuchi
- Journal Title
  
  Kyungpook Mathematical Journal 48-1
  
  Pages: 15-24
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540146
[Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008
- Author(s)
  堀内利郎
- Journal Title
  
  Kyungpook Mathematical Journal 48
  
  Pages: 15-24
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540161
[Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008
- Author(s)
  堀内利郎
- Journal Title
  
  Kyungpook Mathematical Journal 48-1
  
  Pages: 15-24
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540146
[Journal Article] Missing terms in Classical Inequalities.2007
- Author(s)
  堀内利郎
- Journal Title
  
  数理解析研究所講究録 1553
  
  Pages: 1-16
- Data Source
  KAKENHI-PROJECT-17540146
[Journal Article] Missing terms in Classical Inequalities2007
- Author(s)
  T. Horiuchi
- Journal Title
  
  Kyoto LTniv ersity. R. I. M. S. Koukyu_roku 1553
  
  Pages: 1-16
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540146
[Journal Article] Missing terms in Classical Inequalites.2007
- Author(s)
  堀内利郎
- Journal Title
  
  数理解析研究所講究録 1553
  
  Pages: 1-16
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540146
[Journal Article] Kato's Inequalities for Degenerate Quasilinear Elliptic Operators2007
- Author(s)
  Horiuchi, Toshio
- Journal Title
  
  Kyungpook Mathematical Journal (未定)
- Data Source
  KAKENHI-PROJECT-17540146
[Journal Article] Erratum to "On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2006
- Author(s)
  堀内利郎
- Journal Title
  
  Journal of Mathematics of Kyoto University (掲載決定)
- Data Source
  KAKENHI-PROJECT-17540146
[Journal Article] Erratum to "On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2006
- Author(s)
  Horiuchi, Toshio
- Journal Title
  
  Journal of Mathematics of Kyoto University 46-1
  
  Pages: 231-234
- Data Source
  KAKENHI-PROJECT-17540146
[Journal Article] Sharp Remainder terms of Hardy-Sobolev inequalities.2005
- Author(s)
  A.Detalla, T.Horiuchi, H.Ando
- Journal Title
  
  Math. J. Ibaraki Univ. 37
  
  Pages: 39-52
- NAID
  130000886481
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540144
[Journal Article] Sharp remainder terms of Hardy-Sobolev inequalities2005
- Author(s)
  Alnar Detalla, Toshio Horiuchi, Hiroshi Ando
- Journal Title
  
  Math.J.Ibaraki Univ. 37
  
  Pages: 39-52
- NAID
  130000886481
- Data Source
  KAKENHI-PROJECT-17540144
[Journal Article] Sharp Remainder terms of Hardy-Sobolev inequalities.2005
- Author(s)
  A.Detalla, T.Horiuchi, H.Ando
- Journal Title
  
  Math.J.Ibaraki Univ. 37(to appear)
- NAID
  130000886481
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540153
[Journal Article] Sharp remainder terms of Hardy-Sobolev inequalities2005
- Author(s)
  Toshio Horiuchi
- Journal Title
  
  Mathematical Journal Ibaraki University 37
  
  Pages: 39-52
- NAID
  130000886481
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540133
[Journal Article] Sharp remainder terms of Hardy-Sobolev inequalities.2005
- Author(s)
  A.Detalla, T.Horiuchi, H.Ando
- Journal Title
  
  Math.J.Ibaraki Univ. 37(印刷中)
- NAID
  130000886481
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540153
[Journal Article] Sharp Remainder terms of Hardy-Sobolev inequalities.2005
- Author(s)
  A.Detalla, T.Horiuchi, H.Ando
- Journal Title
  
  Math.J.Ibaraki Univ. 37
  
  Pages: 39-52
- NAID
  130000886481
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540144
[Journal Article] Missing terms in Hardy-Sobolev inequalities and its application.2004
- Author(s)
  A.Detalla, T.Horiuchi, H.Ando
- Journal Title
  
  Far East Journal of Mathematical sciences 14(3)
  
  Pages: 333-359
- Data Source
  KAKENHI-PROJECT-15540153
[Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2004
- Author(s)
  堀内利郎
- Journal Title
  
  Journal Math.Kyoto Univ. 44-2
  
  Pages: 341-439
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540151
[Journal Article] Missing terms in Hardy-Sobolev Inequalities and its application2004
- Author(s)
  堀内利郎
- Journal Title
  
  Far East Journal of Mathematical sciences(FJMS) 14・3
  
  Pages: 333-359
- Data Source
  KAKENHI-PROJECT-14540151
[Journal Article] Missing terms in Hardy-Sobolev inequalities.2004
- Author(s)
  A.Detalla, T.Horiuchi, H.Ando
- Journal Title
  
  Proc.of Japan Acad., Ser.A 80-8
  
  Pages: 160-165
- NAID
  40006552680
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540153
[Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2004
- Author(s)
  堀内利郎
- Journal Title
  
  Journal Math.Kyoto Univ. 44・2
  
  Pages: 341-439
- Data Source
  KAKENHI-PROJECT-14540151
[Journal Article] Missing terms in Hardy-Sobolev inequalities.2004
- Author(s)
  A.Detalla, T.Horiuchi, H.Ando
- Journal Title
  
  Proceedings of Japan Academy 80 Ser.A
  
  Pages: 160-165
- NAID
  40006552680
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540153
[Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up.2004
- Author(s)
  T.Horiuchi, P.Kumlin
- Journal Title
  
  J.of Kyoto Univ. 44-2
  
  Pages: 341-439
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540153
[Journal Article] Missing terms in Hardy-Sobolev inequalities and its application.2004
- Author(s)
  A.Detalla, T.Horiuchi, H.Ando
- Journal Title
  
  Far Fast Journal of Mathematical Sciences 14(3)
  
  Pages: 333-359
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540153
[Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2004
- Author(s)
  Toshio Horiuchi
- Journal Title
  
  Journal of Mathematics Kyoto University 44
  
  Pages: 381-439
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540133
[Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up.2004
- Author(s)
  T.Horiuchi
- Journal Title
  
  J.of Kyoto Univ. 44-2
  
  Pages: 341-439
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540151
[Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2004
- Author(s)
  Toshio Horiuchi
- Journal Title
  
  Journal of Kyoto Univ. 44・2
  
  Pages: 341-439
- Data Source
  KAKENHI-PROJECT-16540133
[Journal Article] Missing terms in Hardy-Sobolev inequalities2004
- Author(s)
  堀内利郎
- Journal Title
  
  Proceedings of Japan Academy 80・A・8
  
  Pages: 160-165
- NAID
  40006552680
- Data Source
  KAKENHI-PROJECT-14540151
[Journal Article] Missing terms in Hardy-Sobolev inequalities.2004
- Author(s)
  A.Detalla, T.Horiuchi, H.Ando
- Journal Title
  
  Proceedings of Japan Academy 80Ser.A(8)
  
  Pages: 160-165
- NAID
  40006552680
- Data Source
  KAKENHI-PROJECT-15540153
[Journal Article] Missing terms in Hardy-Sobolev Inequalities and its application.2004
- Author(s)
  A.Detalla, T.Horiuchi, H.Ando
- Journal Title
  
  Far East J.Math.Sci.(FJMS) 14-3
  
  Pages: 333-359
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540153
[Journal Article] Missing terms in generalized Hardy's inequalities and its application.2003
- Author(s)
  T.Horiuchi
- Journal Title
  
  J.of Kyoto Univ. 43-3
  
  Pages: 235-265
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540153
[Journal Article] Missing terms in generalized Hardy's inequalities and its application2003
- Author(s)
  T.Horiuchi
- Journal Title
  
  J.of Kyoto Univ. Vol.43 No.3
  
  Pages: 235-265
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540151
[Journal Article] Missing terms in generalized Hardy inequalities and its application2003
- Author(s)
  堀内利郎
- Journal Title
  
  Journal Math.Kyoto Univ 43-2
  
  Pages: 235-260
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540151
[Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application
- Author(s)
  安藤広、堀内利郎
- Journal Title
  
  Journal of Mathematics of Kyoto Unuv. accepted
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540153
[Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators.
- Author(s)
  T.Horiuchi, P.Kumlin
- Journal Title
  
  Kungpook J. 印刷中
- Data Source
  KAKENHI-PROJECT-17540144
[Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators.
- Author(s)
  T.Horiuchi, P.Kumlin
- Journal Title
  
  Kungpook J. (in press)
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540144
[Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators.
- Author(s)
  T.Horiuchi, P.Kumlin
- Journal Title
  
  Kungpook J. (印刷中)
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540144
[Presentation] Improved Kato's inequalities for a quasilinear elliptic operator and relating topics2018
- Author(s)
  Toshio Horiuchi
- Organizer
  ICM 2018 (Rio De Janeiro, Brasil)
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K05189
[Presentation] The equivalences among p-capacity、p-Laplace-capacities and Hausdorff measure2018
- Author(s)
  劉暁静、堀内利郎
- Organizer
  日本数学会年会函数方程式分科会
- Data Source
  KAKENHI-PROJECT-15H03621
[Presentation] Improved Kato's inequalities for a quasilinear elliptic operator and relating topics2018
- Author(s)
  劉暁静、堀内利郎
- Organizer
  Tsukuba Workshop for Young Mathematicians
- Data Source
  KAKENHI-PROJECT-15H03621
[Presentation] The equivalences among p- capacity, p-Laplace-capacities and Hausdorff measure.2018
- Author(s)
  Xiaojing Liu, Toshio Horiuchi
- Organizer
  日本数学会、函数方程式分科会
- Data Source
  KAKENHI-PROJECT-16K05189
[Presentation] p-ラプラシアンを含む精密化された加藤の不等式とその応用2017
- Author(s)
  劉暁静、堀内利郎
- Organizer
  日本数学会、函数方程式分科会
- Place of Presentation
  首都大学東京
- Year and Date
  2017-03-24
- Data Source
  KAKENHI-PROJECT-16K05189
[Presentation] p-ラプラシアンを含む精密化された加藤の不等式とその応用2017
- Author(s)
  劉暁静, 堀内利郎
- Organizer
  日本数学会年会
- Place of Presentation
  首都大学東京南大沢キャンパス
- Year and Date
  2017-03-24
- Data Source
  KAKENHI-PROJECT-15H03621
[Presentation] 加藤の不等式とその周辺2016
- Author(s)
  堀内利郎
- Organizer
  「偏微分方程式および関連する諸問題」研究集会
- Place of Presentation
  茨城大学
- Year and Date
  2016-09-10
- Data Source
  KAKENHI-PROJECT-16K05189
[Presentation] On Kato's inequalities when Δp u is a measure and related topics2016
- Author(s)
  劉暁静, 堀内利郎
- Organizer
  RIMS研究集会「偏微分方程式の解の形状解析」
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2016-11-09
- Data Source
  KAKENHI-PROJECT-15H03621
[Presentation] Remarks on Kato's inequality when $\Delta_pu$ is a measure2016
- Author(s)
  劉暁静、堀内利郎
- Organizer
  日本数学会、函数方程式分科会
- Place of Presentation
  関西大学
- Year and Date
  2016-09-15
- Data Source
  KAKENHI-PROJECT-16K05189
[Presentation] Remarks on Kato's inequality when Δp u is a measure2016
- Author(s)
  劉暁静, 堀内利郎
- Organizer
  日本数学会秋季総合分科会
- Place of Presentation
  関西大学
- Year and Date
  2016-09-15
- Data Source
  KAKENHI-PROJECT-15H03621
[Presentation] Radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p = 12015
- Author(s)
  堀内利郎、千葉奈緒希
- Organizer
  日本数学会（函数方程式分科会）
- Place of Presentation
  京都産業大学
- Year and Date
  2015-09-13
- Data Source
  KAKENHI-PROJECT-24540157
[Presentation] p-ラプラシアンを含む強最大値原理についての注意2015
- Author(s)
  劉暁静、堀内利郎
- Organizer
  日本数学会（函数方程式分科会）
- Place of Presentation
  京都産業大学
- Year and Date
  2015-09-13
- Data Source
  KAKENHI-PROJECT-24540157
[Presentation] Recent progress in Caffarelli-Kohn-Nirenberg inequalities2014
- Author(s)
  Horiuchi Toshio
- Organizer
  ICM 2014（ International congress of Mathematician 2014 ）
- Place of Presentation
  Seoul Korea
- Year and Date
  2014-08-21
- Data Source
  KAKENHI-PROJECT-24540157
[Presentation] On the Symmetry breaking of the non-critical Caffarelli-Khon-Nirenberg type inequalities by a linearization method2012
- Author(s)
  T, Horiuchi
- Organizer
  日本数学会
- Place of Presentation
  東京
- Year and Date
  2012-03-27
- Data Source
  KAKENHI-PROJECT-20540153
[Presentation] On the symmetry breaking of the non-critical Caffarelli-Khon-Nirenberg inequalities by a linearization method2012
- Author(s)
  堀内利郎
- Organizer
  日本数学会
- Place of Presentation
  東京理科大
- Year and Date
  2012-03-27
- Data Source
  KAKENHI-PROJECT-20540153
[Presentation] 重み付きハーディの不等式の精密化に付いて2012
- Author(s)
  安藤広、堀内利郎、中井英一
- Organizer
  日本数学会
- Place of Presentation
  東京
- Year and Date
  2012-03-27
- Data Source
  KAKENHI-PROJECT-20540153
[Presentation] Construction of slowly increasing functions2012
- Author(s)
  安藤広、堀内利郎、中井英一
- Organizer
  日本数学会
- Place of Presentation
  東京
- Year and Date
  2012-03-29
- Data Source
  KAKENHI-PROJECT-20540153
[Presentation] On the Caffarelli-Kohn-Nirenberg type inequalities involving Critical and Supercritical weights2009
- Author(s)
  T, Horiuchi
- Organizer
  姫路研究集会
- Place of Presentation
  姫路
- Year and Date
  2009-02-21
- Data Source
  KAKENHI-PROJECT-20540153
[Presentation] On the Caffarelli-Kohn-Nirenberg type inequalities involving Critical and Supercritical weights2008
- Author(s)
  T, Horiuchi
- Organizer
  日本数学会
- Place of Presentation
  東京
- Year and Date
  2008-09-24
- Data Source
  KAKENHI-PROJECT-20540153
[Presentation] On the Caffarelli-Kohn-Nirenberg inequalities involving Critical and Supercritical weights2008
- Author(s)
  堀内利郎
- Organizer
  日本数学会
- Place of Presentation
  東京工業大学
- Year and Date
  2008-09-24
- Data Source
  KAKENHI-PROJECT-20540153
[Presentation] On the Caffarelli-Kohn-Nirenberg inequalities involving Critical and Supercritical weights2008
- Author(s)
  堀内利郎
- Organizer
  日本数学会2008年度秋期総合分科会
- Place of Presentation
  東京工業大学
- Year and Date
  2008-09-24
- Data Source
  KAKENHI-PROJECT-19540161

1. SHIMOMURA Katsunori (00201559)

# of Collaborated Projects: 15 results

# of Collaborated Products: 0 results
2. ANDO Hiroshi (60292471)

# of Collaborated Projects: 13 results

# of Collaborated Products: 24 results
3. NAKAI Eiichi (60259900)

# of Collaborated Projects: 9 results

# of Collaborated Products: 9 results
4. SUZUKI Noriaki (50154563)

# of Collaborated Projects: 7 results

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5. ONISHI Kazuei (20078554)

# of Collaborated Projects: 6 results

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6. NISHIO Masaharu (90228156)

# of Collaborated Projects: 6 results

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7. 田村英男 (30022734)

# of Collaborated Projects: 6 results

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8. 荷見守助 (60007549)

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9. SATO Tokushi (00261545)

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10. 日合文雄 (30092571)

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11. 松田隆輝 (10006934)

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12. TACHIZAWA Kazuya (80227090)

# of Collaborated Projects: 3 results

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13. ONOSE Hiroshi (80007559)

# of Collaborated Projects: 2 results

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14. HAYASHI Mikihiro (40007828)

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15. HOSHIRO Toshihiko (40211544)

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16. SOBUKAWA Takuya (60252946)

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17. SADASUE Gaku (40324884)

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18. SAWANO Yoshihiro (40532635)

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19. MIZUTA Yoshihiro (00093815)

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20. 松久富美子 (90194208)

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21. 初瀬弘平 (10007552)

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22. YAMAGAMI Shigeru (90175654)

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23. OSHIMA Hideaki (70047372)

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24. TAKANO Katsuo (30007827)

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25. HORIHATA Kazuhiro (10229239)

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26. NAKAZI Takahiko (30002174)

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27. OZAWA Tohru (70204196)

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28. 中村芳昭 (40007555)

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29. 薮田公三 (30004435)

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30. 久保田陽人 (30007538)

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31. 島倉紀夫 (60025393)

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32. 西垣誠一 (10180598)

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33. 米田剛 (30619086)

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34. 倉坪茂彦 (50003512)

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35. 藤間昌一 (00209082)

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36. 宮地晶彦 (60107696)

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Horiuchi Toshio 堀内 利郎

HORIUCHI Toshio 堀内 利郎

堀内 利郎 ホリウチ トシオ

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A new refinement allowing infinite-order degeneration and explosion of weighted classical inequalities and its application to variational problemsPrincipal InvestigatorOngoing

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古典的不等式の精密化に基づく非線型楕円型方程式の定性的研究Principal InvestigatorOngoing

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実解析・調和解析に由来する関数空間の理論の深化と応用Ongoing

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Refinement of classical inequalities and its application to elliptic variational problemsPrincipal Investigator

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On the improvement of classical inequalities and its applications to nonlinear degenerate elliptic equationsPrincipal Investigator

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On the linearization of quasilinear degenerate elliptic equations and the structure of singular solutionsPrincipal Investigator

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Horiuchi Toshio 堀内利郎

HORIUCHI Toshio 堀内利郎

堀内利郎ホリウチトシオ